# Introductory Statistics

Douglas S. Shafer, University of North Carolina

Zhiyi Zhang, University of North Carolina

Copyright Year: 2012

ISBN 13: 9781453344873

Publisher: Saylor Foundation

Language: English

## Formats Available

## Conditions of Use

Attribution-NonCommercial-ShareAlike

CC BY-NC-SA

## Reviews

The text covers all material needed for an introduction and intermediate statistics course: starting with descriptive statistics, then the elements of probability theory needed for statistics, and finishing with a large portion dedicated to... read more

The text covers all material needed for an introduction and intermediate statistics course: starting with descriptive statistics, then the elements of probability theory needed for statistics, and finishing with a large portion dedicated to inferential statistics, where all topics of hypothesis testing and regression are covered.

I am using this textbook as a second resource for an applied and computational statistics course (mainly for life sciences) with the use of technology (R). The textbook is suited for a statistics course for a general audience and without statistical software (like R). Therefore, the inferential statistics portion of the textbook relies heavily on the use of tables and on the rejection regions instead of the p-value. Also, the pooled variance is used for the testing hypothesis for the difference in means, which doesn't match the results that one can obtain using a statistical software (R), where the unpooled variance is used, and the degrees of freedom for the t-curve is not the typical approximation (sum of the sample sizes minus 2). Moreover, in many real-life data examples, the sample size are slightly higher than 30, but not large enough where using the normal distribution provides precision (instead of using the t-distribution).

The contents is overall up-to-date, but the trend of using technology is increasing and application of statistics to real-life data is increasingly incorporated in statistics courses, including technology component (R is an open and free statistical software used by many data scientists, and life scientists) seem to be inevitable in order for the textbook to remain relevant.

The text is clear, examples are well designed, and the graphics provided in the text are of very good quality.

The text is internally consistent.

The sequencing of the chapters and the sections of each chapters work well. One can use independently a portion of the textbook easily as it used standard notation and widely used terminology.

The sequencing and the organization of the text is clear and logical.

No issues with the interface and no issues with images.

Text is free of grammatical errors.

No noticed issues.

This is a very good introductory and intermediate statistics one-semester course. Content is comprehensive and its sequencing is logical. The exercises at the end of each section are balanced, starting with direct testing of the methods to application of statistics to real-life data. Moreover, solutions to half of the problems are provided (odd numbered problems), and even-numbered problems are fairly similar to the odd-numbered ones, which should allow students to work independently. My only concern with the textbook is that it is well written for a course that doesn't use technology (statistical software) for the inferential statistics, and thus many of the inferential statistics methods are relying on probability tables (focus on rejection regions instead of p-value, using pooled variance, approximate degrees of freedom). This being said, I use this text as a second textbook for a course tailored for life sciences with the use of technology.

Overall the book is quite solid. few things: no permutation/combination for Binomial Distribution, no example for using second method no Poisson distribution, no normal approximation for Binomial and Poisson distribution Section, 7.2 maybe... read more

Overall the book is quite solid.

few things:

no permutation/combination

for Binomial Distribution, no example for using second method

no Poisson distribution,

no normal approximation for Binomial and Poisson distribution

Section, 7.2 maybe mention t distribution as the name of the section

also

could spent more time about how to use those tables

maybe more software technology

no index , no glossary

definition is accurate and well explained

quite solid.

Well explained, though maybe could use some more interesting examples; and maybe could use some definitions comparison etc.

Yes, it is consistent

I think so, it is good

quite standard

quite standard, of course could add some interactive links.

very solid

I didn't notice any offensive example, actually this book seems to have less word problem/example than other books.

Overall it is quite a good book, maybe adding some more fun examples, or more technology for this course.

The text includes the usual topics for a one-semester course in the same order as many introductory statistics texts. Topics are well motivated and discussion usually includes useful diagrams or graphs when appropriate. Each section includes a... read more

The text includes the usual topics for a one-semester course in the same order as many introductory statistics texts. Topics are well motivated and discussion usually includes useful diagrams or graphs when appropriate. Each section includes a sufficient number of exercises. Neither of the pdf or html versions has an index. Users can conduct a word search but that can be awkward. Some topics are missing (e.g., midrange and midquartile for measures of center, how to find percentiles other than quartiles) but it is not uncommon to find lack of coverage of some topics in similar texts. Instructors who are familiar with the American Statistical Association's Guidelines for Assessment and Instruction in Statistics Education (GAISE) will find this text appropriate for meeting the first three of six recommendations and all of the goals set out in this report.

The content is accurate. I did not find any errors in the formulas, but the notation and terminology are sometimes non-traditional. For example, in hypothesis testing the level of significance is included as part of the alternate hypothesis rather than as a separate step in the testing process. As another example, residuals in regression analysis are referred to only as "errors." A third example is the method the authors use for determining if the sample size is large enough for conducting inference for a proportion. Like these examples, most of the other unusual features are minor in impact so that instructors can work around them. Solutions for the exercises at the end of each section appear to be error-free.

The content is current with the traditional, non-randomization, approach to statistical inference. The authors present the same formulas that are used in other similar texts. As mentioned above, instructors who want to follow first three of the six recommendations in the GAISE guidelines will be able to do so using this text.

The text is very easy to read and the authors have provided good motivations for why and how the statistical methods are used. Each section begins with a short list of learning objectives and ends with a list of key-take away concepts. Definitions are set off from the text in boxes. The authors have done a good job in the first chapter of setting the stage to learn statistics. Throughout the text the authors provide explanations of how data is presented and used. New concepts are well-explained and, in most cases, useful diagrams or graphs are included to support the explanations. The use of formulas is demonstrated well.

The text is internally consistent. When the authors refer to topics covered in previous sections they include links to those sections for easy reference. The links appear to be working correctly.

The Table of Contents in the html version allows for easy access to any section of the text. (I did not see a TOC in the pdf version, however.) The authors have divided up some topics into multiple sections, which might make it easier for students to learn. There is just one link to the appendix that contains the normal, T and other tables, rather than separate links for each table. This is awkward but not too problematic. Like some other authors, the authors of this text have chosen to cover inference for a mean before inference for a proportion. And like other texts, the authors don't provide as much detail about inference for a proportion as they do about inference for a mean. If instructors want to cover inference for a proportion before inference for a mean, they would find it difficult to use this text. But, this is the same problem instructors have with other similar texts.

The authors have chosen to cover topics in the same order as many other statistics texts. For example, regression analysis is covered in a chapter later in the book after introducing statistical inference. Instructors who want to cover correlation and regression earlier in the course, however, would be able to do so by skipping the section on inference for the slope.

There are some large gaps between the numerator and denominator in some formulas that might cause confusion. Also, none of the links to the large data sets exercises were working.

No grammatical errors were found. Explanations of statistical concepts are easy to understand and well motivated.

The authors have chosen topics for examples and exercises that are typical of this kind of text. These topics would be of interest to students and are appropriate for demonstrating the usefulness of statistics.

Students may like that the solutions to exercises are provided immediately after the exercises, but I think most faculty would prefer that they were less accessible.

This text covers all the necessary points in an introductory Statistics glass with a well organized, user friendly index. Each chapter has a nice summary of the glossary of terms. read more

This text covers all the necessary points in an introductory Statistics glass with a well organized, user friendly index. Each chapter has a nice summary of the glossary of terms.

The content is accurate and error free. The only comment I have is the notation is different than some textbooks so if using this as supplementation the faculty member make adaptations.

Text concepts are current and could easily be tweaked in the future to prevent becoming a rather "dated" tool.

The text is very clear but my recommendation would be to stick to traditional notation for some ideas.

The book is very consistent with mathematical notations and the framework seems to follow the same format from chapter to chapter. Consistent with math notation is very import so it is positive to see this in this condensed stat book.

It would be very simple for a faculty member to select portions of the text and reorganize as needed.

Although a few items were placed in a different position from standard Statistic books, the flow was logical. For example, the Empirical rule is introduced later than traditional textbooks but blended well with the normal curve discussion.

I actually looked at a few other math books online and decided to review this one. I was pleasantly surprised how easily it was to navigate, click on tables and refer back to formulas.

The text appeared to grammar free.

This text was not culturally insensitive or offensive in any way but I do think it could have been a little more culturally diverse in it's examples.

This book is an excellent resource for students. This would make a very good supplement to another text and is very reader friendly. I would suggest the homework exercises be numbered if possible so if a student had a question, it would be an easy reference point. I also think if the graphing calculator ideas are going to be used, a few diagrams feature a "screenshot" of the calculator screen would be appropriate. I especially like the answers to problems being easily accessed with the click of a button rather than flipping to the back of the book. Many times in class, student's won't even check the answers in the back of the book although attempting the homework! The review section for the course at the end of the book is very appropriate for the students at our institution and the answers are easily located. This is a huge perk.

Finally, I think this book has a great organization, nice examples, and almost a "workbook" approach to the homework helping students step by step. Aesthetically, the book could use a few modern edges to make it easier for the student. This might include an idea such as highlighting important formulas so it stands out.

When comparing numerous statistical textbooks to this book, the level of comprehensiveness is consistent with other material published and in some cases such as the use of examples it is actually more comprehensive than many of the published... read more

When comparing numerous statistical textbooks to this book, the level of comprehensiveness is consistent with other material published and in some cases such as the use of examples it is actually more comprehensive than many of the published statistics textbooks for an introductory class. When I look for an introductory statistics textbook, I look for a book to include topics beginning with introductory descriptive statistics and transitioning into population sampling distribution and basic probability, and concluding with nonparametric and parametric inferential testing. This textbook does a great job transitioning from statistical topics and provides a robust discussion on each topic with a plethora of example problems and practice problems along with answers. Providing answers within a textbook is a plus because most other textbooks make you buy a solutions book, adding to unnecessary costs. Additionally, the authors have done a good job to list an index and glossary to assist in locating various sections within the text with ease.

I have utilized many introductory statistical textbooks in the past and have checked the content within this book with others and have found that the content is accurate. There appear to be no major problems with the theoretical information provided and the example problems associated with each chapter are error-free and consistent with the types of example problems in other textbooks. There also appear to be no major flaws with the solutions to the practice exercises.

Given that this is an introductory statistics textbook, many of the theoretical topics such as formulas, definitions, concepts, etc. covered will not change over time and as a result this text book will not need to be altered within a short period of time. I currently use many textbooks for introductory statistics that are over 5 years old to write lecture slides and generate example problems and have found that many changes were not needed when using older books. This textbook has done a great job to introduce various topics in a robust manner and thus will not need too many updates. The only updates that could potentially be made over time are the use of new and more relevant real-world examples than what the text currently presents. The book is organized so well that it would be extremely easy to add new information or modify existing information very easy without disturbing the flow of the content that is currently presented.

This textbook is written in an extremely simplistic manner. The jargon and terminology that is used is explained thoroughly especially as it pertains to definitions and concepts. All terminology is thoroughly explained with extensive narrative and in many cases figures, illustrations, and formulas are use as supplemental references to assist with making topics clear. When comparing this book with other introductory statistics textbooks, the manner in which content is presented and the reading level utilized within each chapter is very comparable and in some cases even more simplistic than other textbooks.

This textbook is extremely consistent internally. Each chapter is arranged in a very similar manner where the learning objectives are clearly stated followed by definitions, theories, or formulas and then a robust narrative. In each chapter, there are use of figures, illustrations, and numerous example problems that walk the reader through step-by-step problem solving strategies. Additionally, the chapters have a list of robust practice problems. Overall, all material presented in each chapter is consistent from chapter to chapter.

The modularity of the textbook is one of the best features that distinguish this book from others in the subject content area. The content for each learning objective is broken up into smaller pieces allowing for easy adoption within a course. Since the topics are broken up on a more granular level, it would be very easy to rearrange subunits without confusing the reader or creating a disconnect in the topics that are being covered. Often times I like to teach a few topics out of order or merge topics within various chapters together in order for me to explain material better. This book allows for me to have this flexibility since there many sub-sections or units. I also appreciate the fact that there are not many run on chapters where numerous topics are all introduced within a given section.

The topics are presented in logical order as necessary for an introductory statistics course. The book begins with descriptive statistics and spread of data and moves into population sampling and introduction to basic probability, followed by inferential statistical testing. This is commonly the flow of many comparable textbooks currently being used in the field.

There are no major navigation issues when I went through this textbook. I appreciate the face that you can download the book in a PDF format. At times it was a bit difficult to read the formulas that were presented in the boxes within some of the chapters, especially when symbols were used. While it was slightly to read at times, it is still manageable and not a major concern.

There were no grammatical errors that were observed when reviewing this textbook. Additionally, there were no major issues found with the example problems or the solutions to the questions within the various chapters.

This is not applicable. This book is consistent with other statistic books of its kind.

This was an excellent textbook and a good alternative to books that need to be purchased at a high cost in student stores. I would recommend this book to be adopted as a cheaper alternative for introductory statistics courses.

I did not see any index or glossary. It covers the basic descriptive statistics, probability, and inferential statistics of an introductory course. There are no permutations and combinations. The binomial distribution is presented as a formula... read more

I did not see any index or glossary. It covers the basic descriptive statistics, probability, and inferential statistics of an introductory course. There are no permutations and combinations. The binomial distribution is presented as a formula without motivation for where the formula comes from. The normal approximation to the binomial distribution with continuity correction factor is not presented. (Of course, it uses the normal distribution for confidence intervals and tests of hypotheses for proportions later.)

The text does not cover bar charts or pie charts. It does not discuss how to build histograms because software will do that.

It is a comprehensive text, but goes light on (or omits) some topics which some instructors would like to cover.

It has a good selection pf problems, including answers to the odd numbered problems.

On p. 381 it uses p-hat instead of p-nought to determine how large n must be for a test of hypothesis for a proportion. It says you can use the normal distribution instead of the t-distribution if n > 30 (It has the standard table of the t-distribution for up to 100 degrees of freedom).

I find it annoying that the authors expect the student to use the computationally efficient formulas for the variance, correlation, etc.

Otherwise, it is a standard introductory statistics book with standard problems.

I found no problem with the writing of the text.

Yes, it is consistent (including reliance on the computationally efficient formulae which I do not like).

I used it as a pdf, hence am not sure how it could be modified. But like any good statistics book, each chapter is broken down into sections for each topic. You can easily identify the pages where a topic is presented.

It is the standard organization for an introductory statistics text. Correlation and regression are at the end; that is where I cover it even in texts where it is chapter 4.

I used it as a pdf, I am not sure whether there is an interactive version. The graphics were fine, and it has the standard graphiccs for the normal distribution, confidence intervals, and tests of hypotheses. There were acouple of typos like x-bar with the bar after instead of above the x in one place,but that was not a significant problem.

I had no problems with the grammar.

I did not notice any cultural relevance built into the text. It is a statistics text, which is not highly dependent on culture.

It is a basic introductory statistics text, but you should be prepared to supplement it if it misses a topic you like to cover. The most annoying thing I find is the reliance on the computationally efficient formulae for the variance, etc.

The text covers some of the areas needed for an Introduction to Statistics or Elementary Statistics. For example, experimental design was not well covered in chapter 1 which introduction to Statistics. Both the table of content and index was... read more

The text covers some of the areas needed for an Introduction to Statistics or Elementary Statistics. For example, experimental design was not well covered in chapter 1 which introduction to Statistics. Both the table of content and index was missing in this text, which makes it hard to know exactly what page you have to go and read the topic you want to. Lastly there was no set of instruction teaching students how to use technology to perform some of these computations.

I found the contents in the book to accurate and unbiased. I didn’t find any errors or inaccuracies.

Because of the well-structured contents in the textbook, it will be very easy to update it or make changes at any point in time. The content in textbook is up to date.

The clarity in the book was very good for an intro to statistics course. The textbook is easily readable and the graphics are not bad at all. The language in the book is easily understandable. I found most instructions in the book to be very detailed and clear for students to follow.

The contents in the book is very consistent from beginning to the end. The contents in the book are well structured and well organized for each unit.

The text is well sectioned into parts for students to read and understand. This textbook is highly modular, such that instructors combine or use different sections to teach the class and the students will still understand the material at a higher level.

The textbook is well structured and well organized

The interface of the book is very good, however the graphics could have been improved by adding some good images and diagrams. There was no table of contents or index in the pdf version of the book. You can only see the table of contents through online, which would be a very hard to navigate to the appropriate chapters and sections in the book.

No grammatical errors were found.

I did not find any offensive cultural language in the textbook.

On the whole, the textbook would be a very good book to use for an introduction to statistics class or elementary statistics, however I would recommend the authors adding an in-depth experimental design contents to Chapter 1. Secondly I would recommend the authors to add a table of content and an index to the textbook.

The consensus introductory statistics curriculum is typically presented in three major units: (1) Descriptive statistics and study design (first third of course), (2) Probability and sampling distributions (second third of course), and (3)... read more

The consensus introductory statistics curriculum is typically presented in three major units: (1) Descriptive statistics and study design (first third of course), (2) Probability and sampling distributions (second third of course), and (3) Statistical inference (final third of course). This textbook covers all of these topics. Topic 1 is chapters 1 and 2. Topic 2 is chapters 3 through 7. Topic 3 is done in chapters 8 to 14. There are more chapters on the third topic. Inevitably instructors might not use them all. Each chapter comes with plenty of exercises and exercise answers. There is a good index and glossary. The coverage in each topic is very competent and clear. There is, however, nothing exciting or novel in the the manner in which the topics are covered or the pedagogical approach. Recent trends in teaching introductory statistics have emphasized statistics as a part of scientific investigations. So they have integrated the learning of statistics into the understanding of science. This text does little of that. An emerging trend is to make heavy use of computer simulation and even physical simulation techniques to aid learning. This text does none of that.

Content is very competent, accurate, error-free, and unbiased. Instructors will find the many exercises are US-centric. They may find they want exercises that are not that.

The content is fairly timeless in its coverage. It is certainly arranged in ways that would make altering it -- for example, to update it or make less US-centric it -- pretty straightforward.

The textbook is very clear. The writing style is quite accessible. Many of our students do not have English as a first language. It doesn't look like the text would present issues for their understanding. On the other hand BCCampus might consider having the textbook translated into other languages as its contribution.

The use of statistics terminology is consistent through the text. The organization of material is similar in each chapter

The textbook is broken into smaller chunks. It looks like an instructor could skip or reorder sections without there being a problem.

The writing in this text is clear and the organization of material is logical

The text looks like a professionally published textbook. There isn't color and there aren't images. But in other respects it looks good. There aren't any navigation or user interface issues.

I could find no grammatical or spelling mistakes in this text.

The text is not culturally offensive in any way. The examples and exercises are often US-centric. rtsInstructors might want to adapt or modify these parts for a BC or Canadian audience

As previously noted many examples and exercises are US-centric. There is no investigation of causal studies. This something some although not all introductory statistics cover.

This review originated in the BC Open Textbook Collection and is licensed under CC BY-ND.

Most introductory statistics texts use the logical structure of descriptive statistics, probability, and inferential statistics to deliver the materials to new students. This Introductory Statistics textbook by Shafer and Zhang is no exception.... read more

Most introductory statistics texts use the logical structure of descriptive statistics, probability, and inferential statistics to deliver the materials to new students. This Introductory Statistics textbook by Shafer and Zhang is no exception. There is an introduction chapter (chapter 1) that sets out the main definitions and conceptual foundation for the rest of the book. Descriptive statistics is covered in one chapter (chapter 2). Probability and related concepts are covered across four chapters (chapters 3-6). Inferential statistics (chapters 7-9) and their applications to statistical model building and testing (chapter 10-11) form the remaining parts of the content. Collectively these topics form a useful (and standard) foundation for learning statistics. The online version of the text contains a detailed and functioning hyperlinked Table of Contents for the Chapters and Section headings. I was unable to find a glossary or index, but maybe the same functional benefits can be obtained by clicking on the appropriate topic hyperlink and scrolling through the text. One aspect of the content that might be useful to include is the bigger picture notion of: How is statistics used in the real world? The examples and exercises sections provide some hints to students, but contemporary issues such as population growth, climate change and sea level rise are hardly ever mentioned. Including these issues and a connection to the statistical tools that can provide solutions to these problems would help make statistics fun for multidisciplinary students who often perceive statistics as boring and irrelevant. Another aspect of the content is the heavy reliance on the use of a calculator to perform many of the statistical calculations. Whilst this may have some value in terms of flexibility for the instructor as stated by the authors in the Preface, the reality is that once students pursue further statistics and other related courses they will be confronted with the needed to use computer software tools. Including this explicitly would have made the book more comprehensive and relevant to the modern statistics student. It should be noted that in the Large Data Set Exercises sections of the book there are some links to digital spreadsheet data that can be articulated as computer-based data analysis practice for students.

The contents are free of errors. In the Acknowledgments section the authors listed at least 16 individuals linked to higher education that have provided feedback and suggestions for improving the materials. This adds confidence in the quality of the materials. Many of the exercises and examples use concepts (SAT scores for example) and data that are best understood within the context of the United States. Using the textbook outside of that geographic context may prove to be a limitation in terms of asking students to grasp an understanding of the problem domain before attempting a statistical solution. However, there are a few examples that attempt to break the mold - Section 2.5, Application 20 outlines a problem related to hockey pucks.

The statistical core that the textbook focuses on is relatively stable and so changes would be few and far between. This statistical core is up-to-date. The examples and exercises that wrap around the statistical core could use some modifications. For example, issues (climate change, population growth, etc.) that appeal to a wider background of multidisciplinary students can make the entire book more relevant. Making these changes to the existing online HTML files would be relatively easy and straightforward to implement.

The text is written in simple and clear prose. There are hardly any sentences more than 20 words long making the statistical messages easily digestible to students whose first language may not be English. Highlighted definition boxes and key takeaway boxes provide adequate explanations of terminology and key points.

The quality, layout, terminology, sections and overall value of each chapter are all internally consistent. The online Table of Contents also provide a consistent means to access these materials in an easily accessible way.

The text is highly modular. Each Chapter is broken down into smaller sections, and on the whole the materials are covered in a very efficient way making the chapters and sections relatively short. The Chapters are self-contained and can be re-ordered down to the Sections level to suit the needs of the instructor/curriculum.

The topics are arranged in the standard statistical workflow process of Descriptive/Probability/Inferential/Modeling stages. There are a few instances where there is overflow of the topics from one chapter into another where it might not be a good fit. For example, an introduction chapter (Chapter 1) begins immediately to define core statistical concepts and to start familiarizing students with data presentation. The authors chose to continue data presentation (mainly histograms) in chapter 2 that has been titled Descriptive Statistics. In order to avoid any confusion in the minds of students, it would have been useful to focus the Descriptive Statistics chapter on mean, median, mode concepts. The histogram material could have been merged with the data presentation materials of Chapter 1, and maybe added newer presentation forms such as maps and sparklines, to have a more comprehensive data presentation chapter. Experience has shown that chunking materials using clearly defined boundaries help students to learn better. A particularly useful feature is the learning objective that has been given for each Section.

The interface is well designed and organized to enable easy access and pleasing display of the materials. There is some color used throughout the text and this adds to improve the readability and contrast of the images and texts. It is fair to say that figures (especially graphs) are used extensively to illustrate the concepts being discussed.

There is no evidence of grammatical errors. However, it should be noted that the online version of the material seems to be of the highest quality - the printed version of the book (of which I had access) had some symbols missing (Section 10.3) which might be due to the printing/conversion of certain of the Greek symbols used to represent statistical parameters.

There is no evidence that the text is culturally insensitive in any way. I suspect that the book was designed to be used in the United States and so many of the examples are within that context. If the book is to be used for a student population outside of that context, then some changes (either by the authors or instructors) in the diversity of examples will be needed.

Overall, this is a useful book. It does a good job at covering the breadth and depth of the topics one would expect for an introductory course. The content is well presented and easily accessible. The drawback is that statistical computing is not adequately emphasized and that students in Canada will find it a challenge to relate to some of the US-context questions and examples. Some immediate updates that are needed would be: (1) modify chapter 1 to show the links between statistics and real world solutions, (2) directly introduce computer software into the exercises, (3) adapt the questions and examples to be more relevant to an international audience.

This review originated in the BC Open Textbook Collection and is licensed under CC BY-ND.

The text covers some of the areas of the subject, albeit not in-depth. Whether this approach is appropriate for an introductory course, depends on the plan for the further study. Similarly to many other introductory textbooks, the text leaves open... read more

The text covers some of the areas of the subject, albeit not in-depth. Whether this approach is appropriate for an introductory course, depends on the plan for the further study. Similarly to many other introductory textbooks, the text leaves open the question "why" do the particular formulas apply. Glossary is not provided other than chapter-by-chapter.

The authors have gone great lengths towards ensuring error-free and unbiased content. As always in a text of this size, some errors would still creep in despite the best efforts. In particular: 1. Position of the mean on the illustration of a bimodal distribution (page 92) is incorrect. FWHM [full width at half maximum] and the variances for both Gaussian components of the distribution are identical, but the components have different amplitudes. As FWHM is identical, the mean should lie closer to the peak of the component with higher amplitude. Note, that if the FWHM of the left component was twice the FWHM of the right component, the position of the mean would nearly halfway between the modes. 2. Pages 224, 614: pictures and text inside are presented as mirror images of proper orientation. 3. Multiple pages: Authors use Gaussian distribution plots to illustrate Student distribution. While technically correct for large N, this gives a wrong impression about the shape of the Student distribution.

Content is marginally up-to-date. No attention is given to non-parametric methods, Bayesian estimation, multivariate distributions, to name a few areas. The amount of included exercises is unnecessarily overwhelming, making the text appear much longer than it actually is, and difficult to locate the actual text material. Examples are easy to update, but would benefit from reduction of their count. The text will not become obsolete any faster than similar introductory statistics books.

The authors have done a very good effort towards producing an easily readable and accessible text. However, the reader in most cases has to trust the word of the text as not a single proof is presented - even when this would be easy to achieve (Chebyshev theorem). This is a problem with similar introductory statistics textbooks that assume no prior knowledge of algebra.

The text is quite consistent in its terminology and structure. However, the level of detail in presentation of the starting chapters much exceeds that for the last chapter (ANOVA).

The text is clearly intended to be used in a sequential manner as it builds upon the prior knowledge chapter by chapter. Thus, it is better suited to truncation at the end rather than re-organization or dropping of the intermediate subunits.

Topics in the text are presented clearly but require a leap of faith on the part of the reader in every instance a new formula is presented.

The text has some inconsistencies in the layout of its components: 1. Overscripted variables are not typeset well in Word. 2. Formulas and text typeset in LaTeX on occasion import into Word with a loss of resolution (see the example 21, page 93). 3. As noted before, illustrations are heavy on the Gaussian distribution images, even where the Student distribution images are needed. 4. Navigation through the parts imported as images is visibly different from navigation through the parts entered as text.

Grammar has been very well proof-read.

The text is not culturally offensive or insensitive, and makes use of inclusive examples.

The text presents a good attempt at presenting the introductory statistics topics for students with little previous experience with statistics and probability.

This review originated in the BC Open Textbook Collection and is licensed under CC BY-ND.

## Table of Contents

- Chapter 1: Introduction
- Chapter 2: Descriptive Statistics
- Chapter 3: Basic Concepts of Probability
- Chapter 4: Discrete Random Variables
- Chapter 5: Continuous Random Variables
- Chapter 6: Sampling Distributions
- Chapter 7: Estimation
- Chapter 8: Testing Hypotheses
- Chapter 9: Two-Sample Problems
- Chapter 10: Correlation and Regression
- Chapter 11: Chi-Square Tests and F-Tests

## Ancillary Material

## About the Book

In many introductory level courses today, teachers are challenged with the task of fitting in all of the core concepts of the course in a limited period of time. The Introductory Statistics teacher is no stranger to this challenge. To add to the difficulty, many textbooks contain an overabundance of material, which not only results in the need for further streamlining, but also in intimidated students. Shafer and Zhang wrote Introductory Statistics by using their vast teaching experience to present a complete look at introductory statistics topics while keeping in mind a realistic expectation with respect to course duration and students' maturity level.

Over time the core content of this course has developed into a well-defined body of material that is substantial for a one-semester course. Shafer and Zhang believe that the students in this course are best served by a focus on that core material and not by an exposure to a plethora of peripheral topics. Therefore in writing Introduction to Statistics they have sought to present only the core concepts and use a wide-ranging set of exercises for each concept to drive comprehension. As a result Introduction to Statistics is a smaller and less intimidating textbook that trades some extended and unnecessary topics for a better-focused presentation of the central material.

You will not only appreciate the depth and breadth of exercises in Introduction to Statistics, but you will also like the close attention to detail that Shafer and Zhang have paid to the student and instructor solutions manuals. This is one of few books on the market where the textbook authors have written the solutions manuals to maintain the integrity of the material.

In addition, in order to facilitate the use of technology with the book the authors included “large data set exercises,” where appropriate, that refer to large data sets that are available on the web, and for which use of statistical software is necessary.

## About the Contributors

### Authors

**Douglas Shafer** is Professor of Mathematics at the University of North Carolina at Charlotte. In addition to his position in Charlotte he has held visiting positions at the University of Missouri at Columbia and Montana State University and a Senior Fulbright Fellowship in Belgium. He teaches a range of mathematics courses as well as introductory statistics. In addition to journal articles and this statistic textbook he has co-authored with V. G. Romanovski (Maribor, Slovenia) a graduate textbook in his research specialty. He earned a PhD in mathematics at the University of North Carolina at Chapel Hill.

**Zhiyi Zhang** is Professor of Mathematics at the University of North Carolina at Charlotte. In addition to his teaching and research duties at the university, he consults actively to industries and governments on a wide range of statistical issues. His research activities in Statistics have been supported by National Science Foundation, US Environmental Protection Agency, Office of Naval Research, and National Institute of Health. He earned a PhD in Statistics at Rutgers University in New Jersey.